Weak differential monotonicity and axiomatization of convex combinations of solutions to cooperative games

Zeguang Cui (), Erfang Shan () and Wenrong Lyu ()
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Zeguang Cui: Shanghai University
Erfang Shan: Shanghai University
Wenrong Lyu: Zhejiang Normal University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 33, issue 3, No 3, 489-510

Abstract: Abstract The $$\alpha $$ α -egalitarian Shapley values are convex combinations of the Shapley value and the equal division value. For cooperative games that contain more than three players, Casajus and Yokote (Int J Game Theory 48:979–997, 2019) propose a characterization of the $$\alpha $$ α -egalitarian Shapley values by efficiency, weak differential monotonicity, and the average dummy player property. However, it remains an open question whether the characterization holds true for games with three players or not. In this paper, we answer this question in the affirmative. Furthermore, we establish a new axiomatization of the $$\alpha $$ α -equal surplus division values, which are convex combinations of the equal surplus division value and the equal division value.

Keywords: TU-game; Axiomatization; Convex combinations of values; Weak differential monotonicity; 91A12; 91A43; 05C57 (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11750-024-00686-8

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